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Claude Shannon: the man who failed to transform our understanding of information

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Claude Shannon (1916-2001)

Well, Columbia’s Rob Goodman thinks he did, at Aeon:

Shannon’s ‘mathematical theory’ sets out two big ideas. The first is that information is probabilistic. We should begin by grasping that information is a measure of the uncertainty we overcome, Shannon said – which we might also call surprise. What determines this uncertainty is not just the size of the symbol vocabulary, as Nyquist and Hartley thought. It’s also about the odds that any given symbol will be chosen. Take the example of a coin-toss, the simplest thing Shannon could come up with as a ‘source’ of information. A fair coin carries two choices with equal odds; we could say that such a coin, or any ‘device with two stable positions’, stores one binary digit of information. Or, using an abbreviation suggested by one of Shannon’s co-workers, we could say that it stores one bit.

But the crucial step came next. Shannon pointed out that most of our messages are not like fair coins. They are like weighted coins. A biased coin carries less than one bit of information, because the result of any flip is less surprising. Shannon illustrated the point with this graph. You see that the amount of information conveyed by our coin flip (on the y-axis) reaches its apex when the odds are 50-50, represented as 0.5 on the x-axis; but as the outcome grows more predictable in either direction depending on the size of the bias, the information carried by the coin steadily declines.

This is where language enters the picture as a key conceptual tool. Language is a perfect illustration of this rich interplay between predictability and surprise. We communicate with one another by making ourselves predictable, within certain limits. Put another way, the difference between random nonsense and a recognisable language is the presence of rules that reduce surprise.More.

The unfortunate reality is that the vast majority of science writers, while working within an information paradigm even as they write, write as though the Big Fix (the universe as simply matter and energy) is still just around the corner, along with the multiverse and the success of string theory. And the sure-thing tale of human evolution.

See also: Data basic: An introduction to information theory

Introduction to Evolutionary Informatics


New Scientist: Human evolution “more baffling than we thought” (after all this time)

The data processing inequality (DPI), derived from Shannon information, shows any undirected process cannot increase mutual information I(X;Y) between a target (X) and an organism (Y). I(X;Y) = H(X) - H(X|Y) If we say the goal is increasing mutual information between an organism and a complex feature such as an eye, and that evolution is not directed towards producing eyes, then evolution cannot account for complex functionality such as eyes. Say Y is the current generation and Z is the next generation of an organism. The DPI states that if X does not tell us anything about generating Z from Y (i.e. evolution is not directed towards X), H(Z|Y) = H(Z|Y,X), then the mutual information between organism and X can never increase during the course of evolution, I(X;Y) >= I(X;Z). So, evolution, insofar as it is undirected towards complex functionality, cannot account for its occurrence. The information that allows complex functionality, such as eyes, to form must come from outside of evolution. This is really what Dembski's CSI metric and conservation of information boil down to. CSI is the mutual information between the event and the target, and conservation of information says that without impartation of external information (exogenous) about the target, then CSI cannot be increased. So as you can see, Dembski's work is a reformulation of the data processing inequality. EricMH
I think Rob Goodman's article is valuable. He introduces Shannon's use of "weighted" probabilities in Shannon's approach to 'language'---which is what actually occurs in nature. Taking in the bigger sweep of what Shannon is described to have done in this field of language, we see a "non-randomization" of machine language. Human intelligence is used to "constrain" the permissible, and these constraints are applied to an otherwise random process. Hence, the bigger picture Goodmans is giving us is that of 'intelligence' finding a way of overcoming random processes so that "information," as defined by Shannon and accepted by the larger scientific and mathematical community, can be detected; or, to put another way, be "transferred" from one intelligent agent, to another. E.g., if I arrange 50 bricks to form a large SOS, the constraints imposed on the bricks are not of natural, but human, origin, and has a purpose: namely, to "transfer" information from me to possible rescuers. Shouldn't this give us a fairly large hint at what 'information' should look like in general? IOW, in the case that Goodman talks about, the "bricks," i.e., the numbers at first randomly assigned to letters, are 'constrained' in their sequencing based on intelligent instructions to the machine that produces the letters, said instructions taking the form of electronic messages. [This corresponds to my arranging the bricks in such a fashion that SOS is spelled out. What if, instead, I simply took the fifty bricks and threw them randomly in the general area? What would that look like? Would this have anything to do with 'information'? Of course not.] So, what are the elements in this Shannonesque information example? (1) Two (or more) intelligent agents. [Goodman's example: Shannon, and you, the person reading this readout of "letters"=numbers] (2) An element of 'information'.[In Goodman's example, this corresponds to the entire length of the 'letters'] (3) 'Encoding' of this information into physical objects via their sequencing. [In Goodman's example, we see this in "u" coming after "q" and "c" before "k", as well as in certain 'words' coming before others.] (4) Use of physical constraints to "fashion" the 'information.' [In Goodman's example, we see this in the electronic messaging that tells the program how to sequence. The "electronic messaging" constrains what the machine is permitted to do.] In common day experience, this is like me taking a pencil, and writing down a message. The path of the pencil tip is 'guided' by my hand, and constrains the space of the paper so as to convey 'information.' Then, finally, (5) the 'transfer' of information. Without this last step, information cannot exist as an intelligent phenomena. This should be obvious. In fact, all of this stuff should all be fairly straightforward. Boiling down to essentials, here is what we need to have: TWO intelligent agents, and a 'transfer' must take place. If it isn't already obvious, can a monkey tell the difference between what Shannon originally began with in Goodman's example, and the final product? No. It's not intelligent in the ways that humans are: i.e., it is not conscious and free. No 'transfer,' then, can take place if only one side of the 'transfer' is intelligent. Now look at the cell. First, there's the DNA. It is obviously constrained. Just ask Craig Ventnor. [DNA is a product of intelligence in the same way that the final sequence of Goodman's 'Shannon' example is the product of intelligence. Does anyone want to say that the change from the beginning sequence to the final one happened by chance? No.] But, then there's the 'transfer of intelligent information' that must take place. So, we see, let's say, Craig Ventnor is inputting DNA sequence into his primitive bacteria (again, an intelligent 'product'),and must ask: how is his 'information'---already transferred from his learned mind to the nucleotide sequence he's inputting---going to be 'transferred'? Quite simply: it requires another "intelligent" agent. This "intelligent agent" is the splicesome/ribosome, which translates this 'information' into another physical form: proteins, and other cellular products. It is the splicesome/ribosome that is the "other intelligent agent" to which the 'information' in Ventnor's stretch of DNA is 'transferred.' [That Craig Ventnor can communicate with ribosomes means only one thing: the ribosome is an intelligent agent.] So, the question becomes, then, can 'random' mutational processes bring about some physical object capable of 'transferring' INTELLIGENT information to another physical object recognizing this 'transfer.' (BTW, all this talk about entropy as information is no more than the use of a metaphor. In the physical world, where energy is 'transferred' and not information, only human beings, intelligent beings can even begin to process such transfers.) Here's what I wrote about this three years ago. PaV
Shannon is the man who fails to transform your understanding of information if you don't have the math background and motivation to read his published papers. groovamos
The thing you must understand is that Mr. Shannon was originally talking about "signal" and "noise" in WW2 radar signals. Later, he worked for AT&T on digital telephone signals. Reliably sorting Signal from Noise in a VERY narrow context is only distantly related to things like human speech. But the fact that enhancing the quality of radar reception turned out to have direct application to making general statements about human speech and writing says a lot about how humans (who of course created RADAR and digital telephones) create Information generally. That is, having already created written languages, it was simple for humans to create machines that transmit, receive, and display information of interest to humans. Sorting signal from noise is of course a thing that human children learn as they build their vocabulary. Processing signal into information in context (is the wind "blue"? or did the wind "blew"?) requires a fair piece of processing. vmahuna

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